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We explore a geometric approach to generating local SU(2) and $SL(2,\mathbb{C})$ invariants for a collection of qubits inspired by lattice gauge theory. Each local invariant or 'gauge' invariant is associated to a distinct closed path (or…
An analogue of the geometrical optics for description of the modal structure of a wave field in a range-dependent waveguide is considered. In the scope of this approach the mode amplitude is expressed through solutions of the ray equations.…
Orbital angular momentum (OAM), a topological degree of freedom of light, is theoretically invariant under continuous deformations; yet, its physical observability degrades precipitously in complex media, creating a fundamental…
In relation to spatiotemporal intermittency, as it can be observed in coupled map lattices, we study the stability of different wavelengths in competition. Introducing a two dimensional map, we compare its dynamics with the one of the whole…
A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be…
This is a survey article on the stable cohomotopy refinement of Seiberg-Witten invariants containing also new results, for example: - Stable cohomotopy groups describe path components of certain mapping spaces. - Relation of stable…
The transverse spatial attributes of an optical beam can be decomposed into the position, momentum and orbital angular momentum observables. The position and momentum of a beam is directly related to the quadrature amplitudes, whilst the…
Is it possible to modulate the inherent properties of a single light beam, namely amplitude, phase and polarization, simultaneously, by merely its phase? Here, we solve this scientific problem by unifying all these three properties of a…
We present a unified and extended perspective of Bessel beams, irrespective to their orbital angular momentum (OAM) -- zero, integer or noninteger -- and mode -- scalar or vectorial, and LSE/LSM or TE/TM in the latter case. The unification…
A purely analytical extension of the flattened Gaussian beams [Opt. Commun. \textbf{107,} 335 (1994)] to any values of the beam order, is here proposed. Due to it, the paraxial propagation problem of axially symmetric, coherent flat-top…
This paper introduces a novel targetless method for joint intrinsic and extrinsic calibration of LiDAR-camera systems using plane-constrained bundle adjustment (BA). Our method leverages LiDAR point cloud measurements from planes in the…
Recent advances in optical imaging and communication increasingly involve high-dimensional, partially coherent light, creating a growing need for scalable tools to measure and manipulate coherence. Here, we demonstrate the automatic…
Exact solutions describing trapped modes in a plane quantum waveguide with a small rigid obstacle are constructed in the form of convergent series in powers of the small parameter characterizing the smallness of the obstacle. The terms of…
In a recent experiment by Wu {\textit et al.} (arXiv:1511.08170), a Raman-assisted two-dimensional spin-orbit coupling has been realized for a Bose-Einstein condensate in an optical lattice potential. In light of this exciting progress, we…
We present a model that generalizes the Bose-Fermi mapping for strongly correlated 1D bosons in an optical lattice, to cases in which the average number of atoms per site is larger than one. This model gives an accurate account of…
In this paper, we investigate the problem of coordinated path following for fixed-wing UAVs with speed constraints in 2D plane. The objective is to steer a fleet of UAVs along the path(s) while achieving the desired sequenced inter-UAV arc…
We introduce a locally symplectic-invariant quantifier of correlations between two different arbitrary modes in bosonic Gaussian systems, denoted by $\mathcal{D}^{\mathrm{sym}}$. This quantity admits a simple geometric interpretation as an…
We introduce a particle mechanics model with Sp($2M$) gauge invariance. Different partial gauge-fixings by means of sl(2) embeddings on the gauge algebra lead to reduced models which are invariant under diffeomorphisms and classical…
We take advantage of the principal bundle geometry of the space of connections to obtain general results on the presymplectic structure of two classes of (pure) gauge theories: invariant theories, and non-invariant theories satisfying two…
The state of polarization (SOP) is an inherent property of the vectorial nature of light and a crucial parameter in a wide range of remote sensing applications. Nevertheless, the SOP is rather cumbersome to probe experimentally, as…